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Mathematics-Online lexicon:

# Tangent Plane

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Let be a surface implicitely given by the equation

Suppose that is differentiable. Then the tangent plane to at has the equation

provided . Note that the normal vector is parallel to .
In particular for the graph of a function the tangent plane at has the equation

The partial derivative gives the slope of the tangent plane into the direction of the -th coordinate axis.
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